-A Direct Ab Initio Dynamics Study of theWater-Assisted Tautomerization ofFormamide

ROBERT L. BELL, DENI L. TAVERAS, THANH N. TRUONG,JACK SIMONSOepartment oj Chemistry, Ulliversity oj Utalz, Salt Lake City, Utah 84112

Received 24 January 1996; re1.'ised6 November 1996; accepted 7 November 1996

-ABSTRACT: Direct ab initio dynamics calculations based on a canonical variationaltransition-state theory with sewral multidimensional semiclassical tunnelingapproximations were carried out to obtain rate constants for the water-assistedtautomerization of formamide. The accuracy of the density functionals, namely, B-LYP,B3-LYP, and BH&H-LYP, were examined. We found that the BH&H-LYP method yieldsthe most accurate transition-state properties when comparing it to ab initio MP2 andQCISD results, whereas B-LYP and B3-LYP methods predict barrier heights tOGlaw.Reaction path information was calculated at both the MP2 and nonlocal hybrid BH&H-LYP levels using the 6-3lG( d, p) basis set. At the BH&H-L YP level, we found that thezero-point energy fiction lowers the barrier to tautomerization in the formamide-watercomplex by 3.6 kcal/mol. When tunneling is considered, the activation energy at theBH&H-L YP level at 300 K is 17.1 kcal/mol. This is 3.4 kcal/mol below the zero-point-corrected barrier and 7.0 kcal/mol below the classical barrier. Excellent agreementbetween BH&H-LYP and MP2 rate constants further supports the use of BH&H-LYP forrate calculations of large systems. 9 1997John Wiley & Sons, Inc. Int J Quant Chem 63:861-874,1997

Introduction

P roton-transfer reactions are important inmany chemical and biological systems [1-3].A particularly interesting type of proton transfer in

Correspolldmce lo: T. N. Truong.Contract grant sponsor: University of Utah.Contract grant sponsor: National Science FouIldation.Contract grant number: 9116286.

~ 1997 John Wiley & Sens, Inc.

aqueous solution is one in which one or moresolvent water molecules can mediate the processby serving as a bridge that connects the donor andacceptor sites. These water molecules stabilize thetransition stale and therefore substantially lowerthe classical energy barrier to proton transfer. Suchphenomena have been postulated in the action ofenzymes (e.g., carbonic anhydrase [4]) as well as inother tautomerization reactions [5,6]. In this study,we examined the water-assisted tautqmerization offormamide to formamidic acid. This class of reac-

CCC 0020-7608/97/040861-14

BELL ET AL.

tions has importance in protein and pharmaceuti-cal chemistry and provides the simplest model forpeptide linkage [5,7-17]. The NCO backbone offormamide is also found in DNA bases, particu-lady in guanine, cytosine, and thymine. Therefore,formamide ran serve as a model for tautomeriza-tion in these bases.

Several theoretical studies on the monohydratedformamide-water complex have determined thatthe preferred mechanism to forITIformamidic acidproceeds via a stable cyclic double hydro gen-bonded transition staLe [lO, lI, 14, 18-21]. In a pre-vious study (hereinafter referred to as article I) byWang et al. [14], it was found that the tautomeriza-tion of formamide to formamidic' acid [see Fig.Ha)] has a classical barrier of 52 kcal/mol in thegas phase. A single water molecule directly assiststhe tautomerization of formamide by acting as a

,bridge for proton transfer Erom the denar (-NH)to the acceptor (=0) site [see Fig. Hb)] and,consequent1y, lowers the barrier to 26 kcal/mol.Furthermore, it was determined that this water-as-sisted tautomerization proceeds via a concerteddouble proton-transfer mechanism. Structural andfrequency information at the stationary points werealso presented in article I. Adynamical studyonthe similar water-assisted tautomerization of for-

M:

reacta"! produet

(a)

all~

{~~ C\." .°

~reacta"t product

F'GURE1. (a) Formamide gas-phase tautomerization.(b) Formamidewater-assistedtautomerization.

mamidine [6,22] found that both the zero-pointenergy (ZPD and tunneling corrections greatlyatfected the rate of reaction. One ran expectsimilarresults for the water-assisted tautomerization of

formamide; however, a quantitative dynamicalstudy for this system has not been clone and is aprincipal part of this study.

The present wark has twa purposes: (i) to con-tinue the efforts of article I by carrying out accu-rate thermal rate calculations for the forward andreverse reactions of the water-assisted tautomer-

ization of formamide with special attention givento quantal effects, namely, tunneling and zero-point energy motion; and (ii) because use of den-sity functional theory (DFT) ran significantlyredlice the computational dem and for rate cal-culations [23], we test the accuracy of densityfunctional theory (DFT) [6,22,23] for studying re-actions of this type. Comparisons are macie be-tween ab initio, namely, MP2 and QCISD, andDFT methods. The DFT methods utilized are

Becke's (B), the hybrid Becke's half-and-halfmethod (BH&H), and Becke's three-parameter (B3)for exchange energy in combination with thelee-Yang-Parr (LYP) functional for correlationenergy. A smaller number of electronic structurecalculations were also performed for the gas-phasereaction for comparison purposes.

To obtain kinetics information, a conventional

dynamical approach [24] cannot be employed heresince an analytical potential energy function doesnot exist. An alternative is to utilize aur direct ab

initio dynamics approach [25], although other di-rect dynamics approaches such as those discussedin a recent review [26] ran also be used. The directab initio dynamics approach utilized here is basedon a variational trans iti on-s ta te theory (VTST) aug-men ted with multidimensional semiclassical tun-

neling corrections. In this case, geometry, energy,gradient, and Hessian information along the mini-mum energy path (MEP) is calculated direct-ly from molecular orbital and density functionaltheory. Below, we provide a brief overview ofvariational transition-state theory, followed bycomputational details, results and discussion, andsummary sections.

(b)Variational Transition-State Theory

The canonical variational transition-state (CVT)

rate constant for a given temperature is obtained

862 VOL. 63. NO. 4

WATER-ASSISTED TAUTOMERIZATION OF FORMAMIDE

by varying the location of the dividing surfacealong the MEP, whieh intersects and is orthogonalto the MEP, sa as to minimize the number ofrecrossings trajectories [27-29]. The reaction coor-dinate s is defined as the distance along the MEPwith the origin at the transition stale with positivedirection toward the product and negative direc-tion toward the reactant. The generalized transi-tion stale and reactant partition functions ran bewritten as products of the individual electronie,rotational, and vibrational partition functions, withthe assumption that all degrees of freedom areseparabIe. The electronie partition functions forboth the generalized transition stale, and reactantare assumed to rance!. The rotational partitionfunctions were calculated by classieal formulationdue to smalI energy sparing. The vibrational parti-tion functions are treated quantum mechanieallywithin the local harmonie approximation. Notethat the CYT fale theory still treats the reactioncoordinate classieally. To include quantal effects,Le., tunneling, along the reaction coordinate, thefale constant is multiplied by the ground-statetransmission coeffieient [27-29].

Tunneling Methods

The ground-state transmission coeffieient usedhere is defined as the ratio of the thermally aver-aged multidimensional semiclassieal ground-statetransmission probability to the thermally averaged

classical transmission probability for tunnelingthrough an effecti\'e potential which is approxi-mated to be the vibrational adiabatic ground-statepotential curve.

Four approximations for tunneling were used:At the transition stale theory (TST) level of falecalculation, where potential energy information isonly available at the stationary points, the Wigner[30] and zero-curvature tunneling at zeroth-orderinterpolation denoted as ZCT-O [31] are used. TheZCT-O approximation is commonly known asEckart tunneling. The Wigner tunneling correctionassumes that most of the tunneling occurs at thetop of the barrier and is only reasonable at moder-ale to high temperatures. The ZCT -O tunnelingcorrection has been found to be more accurate thanthe Wigner tunneling probabilities due to the useof a one-dimensional Eckart potential curve fittedto the reaction enthalpy at O K, zero-point-cor-rected barrier height, and curvature near the tran-sition stale. Note that the zero-curvature and the

centrifugal-dominant small-curvature semiclassi-cal adiabatie ground-state (CD-SCSAG) approxi-mations are both multidimensional and are used

with CYT fale calculations. For brevity, the zeroand small-curvature tunneling cases are labeledZCT and SCT, respectively. The zero-curvatureapproximation assumes that the tunneling pathfollows the MEP, The SCT tunneling approxima-tion includes "corner-cutting" effects by assumingthe tunneling path to follow the vibrational tum-ing points in the direction of the intemal-centri-

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 863

TABlE ICalculated trequencies (cm -1) ot tormamide.

Reactant Transition stale Produet

Expta BH&H-LYP B3-LYP MP2 BH&H-LYP B3-LYP MP2 BH&H-LYP B3-LYP MP2

289 206.5 149.6 104.4 2117.0; 1912.8i 1972.3i 615.0 589.7 588.8581 588.1 563.0 564.7 490.7 457.5 439.7 651.0 644.8 643.0603 663.5 647.3 649.4 916.6 872.7 877.2 870.8 832.2 848.7

1021 1104.1 1047.0 1058.3 1099.7 1031.3 1038.0 1117.3 1054.2 1063.81046 1108.0 1054.7 1073.5 1161.1 1112.8 1127.5 1127.5 1081.4 1092.81258 1329.5 1275.9 1304.5 1206.1 1165.3 1187.1 1251.5 1200.8 1207.61390 1489.7 1433.7 1459.0 1280.7 1233.5 1267.7 1432.4 1384.6 1398.81577 1687.6 1621.1 1657.8 1534.9 1456.6 1471.6 1479.3 1414.7 1431.41758 1922.5 1836.5 1841.9 1729.0 1659.3 1696.1 1841.5 1750.7 1752.22854 3082.7 2953.1 3067.5 2260.1 2143.2 2186.1 3229.9 3117.7 3221.13439 3729.9 3594.4 3690.9 3276.9 3174.1 3268.7 3669.3 3520.2 3613.33563 3876.1 3738.8 3844.8 3745.0 3581.7 3682.9 3932.0 3739.5 3807.7

"[37].

BELL ET AL.

fugat tarce [28,32]. Thus, the CYT/SCT level rep-resents the most accurate dynamical treatment.Oetailed discussions of both the ZCT and SCT

tunneling approximations are given elsewhere[27-29].

Electronic Structure Calculations

Geometries of the reactant" transition staLe,and product for the tautomerization in the for-mamide-water complex were calculated at theMP2 and quadratic configuration interaction, in-cluding single and double excitations CQCISO),levels of theory and also with B-LYP, B3-LYP, andBH&H-L YP OFT methods. Note that the BH&H-LYP functional as implemented in the G92/0FT[33] is given by

E = O5EHF + O5E S1ater+ ELYPxc . X . X c' (1)

where E~F and E~laterare the Hartree-Fock andStater exchange energies, respectively, and ECYPisthe LYP correlation energy. The double-zeta pluspolarization 6-31GCd,p) basis set was used in aUthe calculations. The MEP at the BH&H-L YP level

was calculated with a step size of 0.1 amu: cbohrfor atotal of 20 steps in each direction Erom thetransition staLe. The MEP at the MP2 le,'el wascalculated with a step size of 0.05 amul/cbohr foratotal of 40 steps in each direction Erom thetransition staLe. Hessian calculations were per-fohned at the MP2 and BH&H-L YP levels at se-

lected points along the MEP. AU the electronicstructure calculations were dane using theG92/0FT and G94 [34] programs.

Rate Calculations

An automated focusing technique [35] \\'as usedto choose a set of 21 points, including the transi-tion staLe, along the BH&H-L YP and MP2 :v1EPsfor which Hessian calculations were carried out.

The focusing technique was designed to minimizethe number of Hessian points on the MEP whilemaintaining a reasonable level of accuracy. Fromaur experience, rate constants with appreciabletunneling contributions require at least 21 Hessianpoints. To check the convergence, we also per-formed a 30-Hessian point-points chosen by thesame focusing technique-rate calculation, at the

864 VOL. 63. NO. 4

TABlE IICalculated frequencies (cm -1) ot the formamide-water system.

Reactant Transition staLe Produet

BH&LH-L YP B3-LYP MP2 BH&LH-L YP B3-L YP MP2 BH&H-L YP B3-L YP MP2

161.3 159.8 144.9 1768.8i 1539.4i 1653.0i 196.2 196.3 188.7

204.8 204.9 191.3 282.7 266.0 267.7 230.2 230.8 216.1

214.9 215.4 205.3 525.5 518.0 524.8 249.9 260.4 244.5

262.9 264.2 251.5 583.6 558.0 567.1 346.8 368.6 340.5

371.3 365.8 354.9 603.8 571.3 590.1 402.6 402.9 385.8

451.8 441.3 424.6 650.1 605.7 623.3 686.6 668.6 658.9

643.6 624.2 616.9 716.7 687.3 708.1 818.7 806.9 793.3

760.8 783.1 745.8 854.6 824.5 825.4 845.7 854.6 832.4

838.7 836.2 815.4 1110.9 1040.1 1053.6 956.5 965.3 943.7

1115.7 1053.3 1070.0 1119.0 1112.9 1125.8 1129.1 1075.6 1086.9

1145.5 1100.4 1111.8 1284.0 1320.8 1336.2 1167.1 1124.6 1131.0

1391.4 1344.3 1364.9 1410.9 1361.4 1389.8 1352.4 1307.5 1312.6

1486.1 1427.7 1454.9 1445.3 1417.1 1444.0 1492.0 1427.1 1445.4

1694.9 1622.8 1659.4 1535.5 1474.4 1508.1 1547.1 1512.8 1515.9

1740.3 1696.2 1717.5 1555.2 1517.1 1561.1 1730.2 1685.3 1706.4

1881.9 1795.9 1820.6 1720.4 1647.8 1676.6 1816.9 1727.8 1743.8

3110.9 2993.6 3096.8 1832.9 1748.2 1784.8 3222.4 3109.3 3210.9

3596.0 3415.7 3566.7 2042.3 1962.0 1994.6 3532.5 3220.7 3422.1

3793.3 3577.9 3721.6 3197.3 3088.3 3185.7 3685.6 3457.2 3621 .2

3842.9 3701.0 3810.1 3761.7 3613.7 3704.9 3719.5 3536.8 3649.4

4044.9 3864.5 3966.7 4010.7 3829.9 3903.4 4037.6 3857.2 3953.5

WATER-ASSISTED TAUTOMERIZATIONOF FORMAMIDE

FIGURE 2. (a) Optimized structural data ot the gas-phase tormamide (reactant) at the MP2, B3-LYP,and BH&H-LYP/ 6-31G(d,p) levels ot theory with experimental data. Bond"lengths ara in angstroms and angles ara in degrees.Experimental values ara taken trom [14]. (b) Similar to (a) except tor produet structure. (c) Similar to (a) except tortransition-state structure.

INTERNATIONALJOURNAL OF QUANTUM CHEMISTRY 865

Reactant

Oeviation from experimentVariabies Experirnen t MP2 BH&H-LYP B3-LYP

N1C2 1.352 0.010 -0.002 0.009C203 1.219 0.005 -0.016 -0.003N1H4 1.002 0.001 -0.005 0.005N1H5 1.002 0.004 -0.002 0.007C2H6 1.098 0.003 0.000 0.011NIC203 124.7 0.1 0.3 0.2C2N1H4 120.0 1.4 1.7 1.7C2N1H5 118.5 0.1 0.4 0.5N1C2H6 112.7 -0.6 -0.3 -0.7

(a)

Produet

Oeviation from MP2Variabies MP2 BH&H-L yP B3-LYP

N1C2 1.274 -0.020 -0.007C203 1.350 -0.017 -0.004N1H4 1.016 -0.008 -0.003N1H5 2.294 -0.006 0.000C2H6 1.088 -0.003 0.006N1C203 121.6 0.7 0.5C2N1H4 110.0 1.3 0.8C2N1H5 54.4 -0.2 0.0N1C2H6 128.1 -0.8 -0.1

(b)

BELL ET AL.

FIGURE 2. (Continued).

MP2 level. We found that at 300 K the CYT/SCTfale eonstants eonverged to within 1.7% for theforward fale. This is a very aeeeptable level ofaeeuraey given that experimental uneertainty isoften larger than 20%.

The c1assieal potential energy barrier for theMP2 and BH&H-L YP fale ealculations wece sealed

faetors of 1.151 and 1.075, respeetively, to repro-duee the moce aeeurate QCISD barrier. TheRate(theoretieal fale) [36] program was used to earryout aU TST and CVT fale and tunneling ealcula-tions.

Geometries and Frequencies

Although the struetures and frequeneies of theequilibrium struetures wece diseussed in detail inartic1e I at the Hartree-Foek level, we have in-cluded the formamide and formamide-water fre-

quencies of the equiIibrium struetures at theBH&H-LYP, B3-LYP, MP2, and QCISD levels oftheory and experiment in Tables I and II, respee-tively. The equilibrium geometries of formamideare of C, symmetry for both DFT methods. At the~1P2 level, the equilibrium strueture was found to

be of CI symmetry. These wece determined Eromfrequeney ealculations which yielded aU real fre-queneies for aU methods. Below, we will foeus aurattention on the aeeuraev of the DFT methods.

Speeifieally for the equilibrium struetures foundin Figures 2(a) and (b) and 3(a) and (b), the B3-LYP,BH&H-L YP, and MP2 struetural data are in over-all very good agreement with the highest level oftheory ar available experimental data. The MP2method is, in general, better than both of the DFTmethods with the largest differenee of 0.059 Aforbond lengths and of 1.40 for angles. As for theBH&H-L YP and B3-LYP methods, their resultseompared equally well with the MP2 and QCISDresults. In particular, differenees for band lengthsrange Erom 0.077 to 0.119 Aand Erom 2.7 to 3.20 forangles for the BH&H-LYP and B3-LYP methods,respeetively. However for the hydrogen-bondedeomplexes [see Fig. 3(a) and (b)], both DFT meth-ods tend to slight1y underestimate band lengths,although the BH&H-L YP method yields better re-sults for aetive bonds, bonds which are eitherbeing formed and broken in the eourse of thereaetion.

To get an idea of the reliability of frequeneyealculations, the averaged unsigned pereent differ-

866 VOL. 63. NO. 4

Transition Stale

Deviation EromMP2 IVariabies MP2 BH&H-LYP B3-LYP

N1C2 1.274 -0.016 -0.004C203 1.350 -0.019 -0.005N1H4 1.016 -0.008 0.004N1H5 2.294 -0.003 0.015C2H6 1.088 -0.003 0.006N1C203 121.6 -0.3 0.0C2N1H4 110.0 0.4 -0.2C2N1H5 105.4 0.2 0.3N1C2H6 128.1 0.1 0.1

(c)

WATER-ASSISTED TAUTOMERIZATIONOF FORMAMIDE

FIGURE 3. (a) Optimized struetural data ot the tormamide-water eomplex (reaetant) at the MP2,BH&H-LYP, B3-LYP,and QCISD/ 6-31G(d, p) levels ot theory. Band lengths ara in angstroms and angles ara in degrees. (b) Similarto (a)exeept tor produet strueture. (e) Similarto (a) exeept tor transition-state strueture.

ences between experimental [37], BH&H-L YP, B3-~ LYP, and MP2 methods for a11harmonie frequen-

cies for the formamide structure were calculated.As can be seen in Table I, BH&H-LYP, B3-LYP,and MP2 methods overestimate the experimentalvalues, excep t for the lowest twa, by unsignedaverages of 9.0, 7.2, and 10.2%, respectively.

The average unsigned percent difference be-tween the MP2, B3-LYP, and BH&H-L YP methodsfor a11frequencies for the formamide-water equi-librium structures were calculated. For these struc-tures, both OFT method overestimate the vibra-

tional frequencies when compared to the MP2method by unsigned averages of 3.1 and 3.2% forthe BH&H-LYP and B3-LYP methods, respec-tively.

For the transition-state structures [see Figs. 2(c)and 3(c)], specifiea11y for the gas-phase system,OFT results are very close to the MP2 ones.o Thelargest deviations range from 0.019 to 0.015 A forband lengths and Erom 0.4 to 0.30 for angles for theBH&H-L YP and B3-LYP methods, respectively. Forthe hydrogen-bonded complex, a11 three methodsare comparable. The MP2 method displays the

INTERNATIONALJOURNAL OF QUANTUM CHEMISTRY 867

Reactant

Deviatian tram QCISDVariabies QCISD MP2 BH&H-L YP 53-LYP

NIC2 1.351 -0.002 -0.014 -0.003NIH4 1.003 0.000 -0.006 0.004N1H5 1.013 0.002 -0.003 0.009C203 1.232 0.004 -0.017 -0.002C2H6 1.099 0.000 -0.004 0.00603H8 1.973 -0.030 -0.058 -0.064HSO7 2.055 -0.038 -0.057 -0.07907H8 0.971 0.003 -0.005 0.00907H9 0.962 0.000 -0.009 0.004N1C2H6 113.6 0.0 0.2 0.2NIC203 124.9 0.0 0.0 -0.1NIH507 140.5 0.2 -0.5 0.4C2NIH4 120.6 0.1 0.3 0.3C2N1H5 118.3 -0.3 -0.3 -0.8C203H8 106.1 -0.6 0.2 -0.6H507H8 79.2 0.2 1.1 0.6H907H5 115.1 -0.4 2.5 -3.2H907H8 104.2 -0.2 1.0 -0.3

BELL ET AL.

largest deviations of 0.034 Afor bond lengths andot 0.80 for angles. Both the BH&H-L YP and B3-LYPmethods yielq deviations in band lengths on the

~ order of 0.03 A and of 1.50 for angles.Average unsigned percent differences between

the MP2, B3-LYP, and BH&H-LYP methods for aUfrequencies for the formamide-water transitionstale yield different results. The BH&H-LYPmethod gives trequencies that are 2.5% greaterthan the MP2 frequencies while the B3-LYP methodgi,'es frequencies smaUer by 2.1%. AU methodsyielded a single imaginary frequency for the tran-sition stale. The MP2 method gave a frequency of

1653i cm -1, the BH&H-L YP method gave oneof 1769i cm -l, and the B3-LYP method gave oneof 1539i cm -l.

Energetics

The reaction energetics tor both the gas-phaseand water-assisted tautomerizations as wen as the

energetics for the formation of these complexes aregiven in Table III. The energetics ot formation ofthe formamide-water and formamidic-water

868 VOL. 63. NO. 4

Product

Deviation EromQCISDVariabies QCISD MP2 BH&H-LYP B3-LyP

N1C2 1.280 0.004 -0.015 0.000N1H4 1.015 0.000 -0.008 0.002N1H5 2.013 -0.059 -0.077 -0.119C203 1.337 -0.003 -0.021 -0.010C2H6 1.089 -0.001 -0.004 0.00503H8 0.974 0.016 0.004 0.024H507 0.962 0.014 0.008 0.02507H8 1.830 -0.053 0.060 -0.09107H9 0.962 0.001 -0.008 0.004N1C2H6 125.5 0.0 -0.5 -0.3N1C203 123.4 -0.1 0.2 0.0N1H507 140.1 0.6 0.9 2.1C2N1H4 110.2 -0.1 1.3 1.1C2N1H5 106.0 -0.3 -0.5 -0.7C203H8 108.1 -0.5 0.9 -0.2H507H8 82.4 0.7 1.0 0.5H907H5 104.6 -0.1 1.2 0.0H907H8 111.2 0.1 2.7 -1.2

FIGURE 3. (Continued).

WATER-ASSISTEDTAUTOMERIZATION OF FORMAMIDE

complexes favor the BH&H-L YP method whencomparisons are macie to the MP2 results for boththe change in total energy, j, E, and the reactionenthalpy at O K, I1Hg. As found in article I , theclassical barrier for the tautomerization in the gagphase is 51.9 kcal/mol at CISD(FULU using theDunning correlation consistent polarized valencedouble-zeta plus basis set [38]. This barrier is low-ered to 26.0 kcal/mol when a single water moleculeis added. Zero-point energy corrections lower thesebarriers by 3.0 and 3.4 kcal/mol tor the gas-phaseand monohydrated cases, respectively.

The BH&H-LYP /6-31G(d, p) gas-phase classicalbarrier ot 51.8 kcal/mol is nearly equal to theCISD(FULL) barrier. Both the MP2 and B3-LYP

classical barriers are approximately 5 kcal/moland the B-LYP is over 9 kcal/mol below theBH&H-L YP and CISD(FULL) barriers. The BH&H-LYP water-assisted classical barrier of 24.1

kcal/mol gives the best agreement with the QCISDbarrier of 25.9 kcal/mol when compared with theMP2, B3-LYP, and B-LYP barriers ot 22.5,19.5, and16.9 kcal/mol, respectively. The BH& H-LYPmethod algo gives the best zero-point-corrected

INTERNATIONALJOURNAL OF QUANTUM CHEMISTRY 869

Transition StaLe

Deviation EromQCISDVariabies QCISD MP2 BH&H-LYP B3-LyP

N1C2 1.310 0.001 -0.014 -0.002N1H4 1.008 0.001 -0.007 0.004N1HS 1.300 0.009 -0.001 0.018C203 1.288 0.001 -0.018 -0.004C2H6 1.091 0.000 -0.003 0.00603H8 1.190 0.034 -0.018 0.029H507 1.190 -0.006 -0.007 0.00207H8 1.208 0.002 -0.003 0.01907H9 0.964 0.002 -0.009 0.003N1C2H6 121.3 0.0 -0.1 0.0N1C203 121.8 0.2 0.2 0.3N1HSO7 148.3 0.1 -0.3 -0.1C2N1H4 116.4 -D.4 0.6 0.2C2N1HS' 105.2 -D.1 -0.1 0.0C203H8 102.7 -0.3 0.8 0.5H507H8 84.8 -0.1 0.1 -0.2H907HS 110.0 -0.8 1.4 -0.9H907H8 109.7 -0.7 1.5 -0.5

FIGURE 3. (Continued).

barriers with differences trom the CISD results

being 0.1 and 2.1 kcal/mol for the gas-phase andmonohydrated systems, respectively.

Minimum-Energy Path

The potential energy along with the correspond-ing structural changes in the formamide-watercomplex along the MEP are illustrated in Figures 4and 5, respectively. This system reveals a con-certed two-stage mechanism in qualitative agree-ment with that for the formamidine-water system[6]. From an examination of the structural changestram reactant to product, it ran be seen that theNCO band angle undergoes compression first, thenthe NH band starts to lengthen. Spedfically, tau-tomerization in the formamide-water system re-

quires the NCO band angle to be compressed byonly 2.9° or 2.3% trom the equilibrium value thenthe NH band is stretched trom an equilibriumvalue of 1.010-1.299 Aat the transition stale, anincrease of 28%.

For tautomerization to occur, the formamide(gas-phase) molecule mus t undergo large struc-tural changes that are energetically expensive. TheNCO band angle is compressed tram an equilib-rium value of 124.8° to 108.6°, a 13% decrease. TheNH band is then stretched Erom 1.006 to 1.320 A,an increase of 31%, to reach the transition stale.The large reduction in the classical energy barrierErom the gag phase to the water-assisted case isattributed to the water acting as a catalyst throughthe stabilization of the transition stale [4-6,14,18,19,22]. Most of the energy savings is achieved

because the NCO angle has to be compressed byonly 2.9° when compared with that for the gagphase which has to be compressed by 16.7°.

The BH&H-L YP and MP2 generalized frequen-des (> 500 cm -1) in Figure 6 show similar results,consistent with the results for the stationary points.In a previous studyon the CH4 + H reaction byTruong and Duncan [39], it was shown in a plot

30 ,

]i

1j

~c..(;CI.

[j

25 ~

'OE::......~

~ 15 i-~cW

20,-

10 -

o-2.0 0.0 0.5 1.0 1.5 2.0-1.5 -1.0 -0.5

s (amu"2bohr)

FIGURE 4. Classieal. VMEP(solid). and zero-pointcorrected. VaG(dotted). potential energy vs. reactioncoordinate for the water-assisted formamide

tautomerization at the BH&H-L YP / 6-31 G(d.p) 'eve!.Circles indicate where Hessians ara algo available.

870 VOL. 63, NO. 4

BELL ET AL.

TABlE III -Reaction energetics for the formamide gas-phaseand water-assisted tautomerizations; all energiesin kcal/mol.

:1E :1Hg :1V. :1Va*G

F + H20 -> F(H2O)B-LYP -13.7 -10.6B3-LYP -13.5 -10.3BH&H-LYP -13.2 -10.1MP2a -12.8 -9.7

FA + H20 -> FA(H2O)B-LYP -16.5 -13.6B3-LYP -16.0 -13.0BH&H-LYP -15.3 -12.2MP2a -14.7 -11.7F -> FA

B-LYP 12.6 13.1 42.4 39.4B3-LYP 12.6 13.2 46.2 43.3BH&H-LYP 12.6 13.2 51.8 48.8MP2a 12.3 12.8 46.8 43.8CISD(FULL)a 11.4 51.9 48.9

F(H2O) ->FA(H2O)B-LYP 9.8 10.1 16.9 13.7B3-LYP 10.1 10.6 19.5 16.2BH&LYP 10.5 11.0 24.1 20.5MP2a 10.5 10.9 22.5 19.2QCISD 10.5 25.9CISD(FULL)a 10.9 26.0 22.6

a[14].

03H8

I 07H8 0...0...0-11261.6, X,'""00 o~ '00'0.. " o '!lo 00 o ,:'\ 000 "

L \ 0'0000 "o /",'~ \ '000 / '~ 1.4;- 000 . /\ /Gl o ,u \ "i ~. o",,' / /'~ - \ 'oot" OCN j

'

o . 00 / '"g 1.2 r \ ."/ / 00 "'00 ~/ Ial ,,00 '/

~ '., 00 I

~

-.\." / 000000/,-,-,;,,""""";' 000'0

1.0

.

- ~ '-.. /' ".. ......................~-- ~ 122, N1H5

1.8 r

0.8

-1.5 01.0 .0.5

WATER-ASSISTED TAUTOMERIZATION OF FORMAMIDE

127

125

»::IlQiD

124Ci:CDlQ;;CD~123

0.0

121

1.50.5 1.0

s (amu'l2bohr)

FIGURE 5, Geometrie parameters vso reaetion eoordinate tor the water-assisted tormamide tautomerization at theBH&H-L YP / 6-31 G(d, p) level. The reader is reterred to Figures 3(a)-(e) for definitions ot band distanees.

similar to Figure 6 that generalized transition-statefrequencies calculated at the BH&H~LYP/6-31lG(d,P) were found to be in excellent agreementwith the QCISD/6-31lGCd,p) resultso

4500 t . , ,

4000 l ., . j-_o::::::::::::::::::::::::~~ ~

"- 3500 ~~ ,e F:-;:'O-~u f -0_-:- ... ~

i 3000 r Vi' .,' j

l 2500 ~ \, ,.- j~ f : 1" t . ~~ 200H -- jID' --- . -1

~ :::: f;;~~:'~

BELL ET AL.

TABlE IV

Rate constants (s -1) for the formamide water-assisted forward reaction at the BH&H-LYPI 6-31G(d, p) level.

shape is shown in the difference between theTST/ZCT-O and CYT/ZCT rate constants. At 300K, the CYT/ZCT rate constant is smaller by afactor of 2.21. This is because the Eckart potentialoften has a too narrow wid th. The effect of "comer

cutting" can be seen in a comparison of theCYT/ZCT and CYT/SCT rate constants. At 300 K,the CYT/SCT rate constant is larger by a factor of2.23. The 30-Hessian point CYT/SCT rate constantat the MP2 level is larger than the BH&H-LYPcounterpart by a factor of 1.67 at 300 K for theforward rate. Recall that both the BH&H-L YP and

MP2 potential curves were scaled to yield theQCISD barrier.

Tunneling effects can be ret1ected through thestrong temperature dependence of the activationenergy, En' which is the slope of Arrhenius curves

(see Table VI). At the most accurate level of rate

theory considered here, namely, the CYT/SCTlevel, the activation energy decreases from 20.7 to13.5 kcal/mol as the temperature decreases from800 to 200 K. At 300 K, the calculated activationenergy is 17.1 kcal/mol. This is 3.4 kcal/mol be-law the zero-point corrected barrier and 7.0kcal/mol below the classical barrier.

Summal'~-

We carried out direct ab initio and DFT dynam-ics calculations on the water-assisted tautomeriza-tion of formamide to obtain canonical rate con-

stants and found many similarities with thewater-assisted tautomerization ot formamidine [6].

TABlE VRate constants (s -1) for the formamide water-assisted reverse reaction at the BH&H-LYPI 6-31G(d, p) level.

CVT I SCTTIK TST TST I W TST I ZCT-O CVT CVT I ZCT CVT I SCT (MP2)a

200 4.58E - 13 3.55E - 12 8.17E - 10 4.49E - 13 3.59E - 11 8AOE - 8 5.93E - 7250 3.02E - 8 1.61 E - 7 2.27E - 6 2.97E - 8 3.19E - 7 2.71E - 6 7.65E - 6300 4.67E - 5 1.87E - 4 7.00E - 4 4.61E - 5 2.07E - 4 4.61E - 4 7.70E - 4350 8.55E - 3 2.74E - 2 5.31E - 2 8A7E - 3 2.40E - 2 3A6E - 2 4.53E - 2400 4.17E - 1 1.12 1.52 4.13E - 1 8.94E - 1 1.08 1.21450 8.45 1.97E + 1 2.18E + 1 8.38 1 .52E + 1 1.70E + 1 1.72E+1500 9.31E + 1 1.93E + 2 1.89E + 2 9.24E + 1 1.48E + 2 1.60E + 2 1.49E + 2600 3.37E + 3 5.89E + 3 4.93E + 3 3.34E + 3 4.62E + 3 4.78E + 3 4.1 OE + 3800 2.98E + 5 4.24E + 5 3.11 E + 5 2.96E + 5 3.54E + 5 3.58E + 5 2.83E + 5

1000 4.47E + 6 5.68E + 6 3.92E + 6 4.45E + 6 4.97E + 6 5.01E + 6 3.80E + 6

"30 Hessian point rate constant.

CVT I SCTTIK TST TST I W TSTI ZCT-O CVT CVTI ZCT CVTI SCT (MP2)a

200 9.00E - 1 6.98 1.61E+ 3 8.84E - 1 7.06E + 1 7.38E + 3 2.24E+ 4250 2.49E + 2 1.33E + 3 1.88E + 4 2.46E + 2 2.64E + 3 2.24E + 4 4.45E + 4300 1.03E + 4 4.13E+4 1.55E + 5 1.02E + 4 4.57E + 4 1.02E + 5 1.31E + 5350 1.45E + 5 4.64E + 5 9.00E + 5 1.43E + 5 4.07E + 5 5.86E + 5 6.27E + 5400 1.04E + 6 2.80E + 6 3.80E + 6 1.03E + 6 2.23E + 6 2.70E + 6 2.59E + 6450 4.80E + 6 1.12E + 7 1.24E + 7 4.76E + 6 8.63E + 6 9.66E + 6 8.65E + 6500 1.62E + 7 3.38E + 7 3.27E + 7 1.61E + 7 2.59E + 7 2.78E + 7 2.39E + 7600 1.01E + 8 1.77E+8 1.48E + 8 1.OOE+ 8 1.38E + 8 1.43E + 8 1.17E + 8800 1.00E + 9 1A3E + 9 1.05E + 9 9.97E + 8 1.19E + 9 1.21E + 9 9.59E + 8

1000 4.09E+ 9 5.19E + 9 3.58E + 9 4.06E + 9 4.54E + 9 4.58E + 9 3.61E + 9

"30 Hessianpoint rateconstant.

872 VOL. 63, NO. 4

20 ~

10

O

~"1;:.5 -10

.20

.301.0 3.5 4.0 4.5 5.02.5 3.01.5 2.0

1000/T

FIGURE 7. Arrhenius plot ot (solid) TST IW. (dotted)TST I ZCT-O, (dash-dotted) CVT I ZCT, and (long-dashed)CVT I SCT calculated at the BH&H-L YP I 6-31 G(d, p)level and (long dash, three dots) CVT I SCT rateconstants calculated at the MP2 I 6-31 G(d, p) level using30 Hessian points vs. 1000 I T (K) tor thetormamide-water complex torward reaction. Both theBH&H-L YP and MP2 potential barriers we re scaled tomatch the QCISD barrier.

25

20

15

'"1;:

.5 1 o

~ ~

5

O1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

1000/T

FIGURE 8. Similar to Figure 7 except tor the reversereaction.

WATER-ASSISTEDTAUTOMERIZATION OF FORMAMIDE

TABLE VIActivation energies (kcal/mol) ot the tormamide-water tautomerization tor the torward and reversedirections calculated at the BH&LH-LYP/6-31G(d, p) level ot theory.

For the formamide-water system, it proceeds via aconcerted two-stage mechanism that involves asmalI compression of the NCO band angle beforechanges in band lengths occur. Water acts as abridge between the denar and acceptor sites asresults field smaller compression of the NCO an-gle and, consequently, lowers the barrier from thegag phase by a factor of 2.1 at the BH&H-L YPlevel. The ZPE motion and tunneling significantlyenhances the proton-transfer fale. In particular, theBH&H-L YP CYT /SCT activation energy at 300 Kis only 17.1 kcal/mol, which is 7.0 kcal/mol belowthe classical. Of this, 3.-t kcal/mol is from the ZPEmotion and 3.6 kcal/mol from quantum mechani-cal tunneling.

We are especially encouraged to see excellentagreement between the DFT and MP2 structuraland frequency data. Particularly for the formamide-water structure, all methods are in excellentagreement with the expensive QCISD method. Theclassical and zero-point energy barriers to tau-tomerization for both the gas-phase and water-assisted cases are best predicted by the BH&H-L YPmethod when compared to the more accurateCISO(FULU and QCISD methods. When takinginto consideration both accuracy and cost, theBH&H-L YP method is the better method com-

pared to the B-LYP, B3-LYP, and MP2 methods forfale calculations.

5.0

.-\CKNOWLEDGi\IEl\TS

This wark was supported by the University ofUtah and the National Science Foundation through

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 873

Forward reaction Ea Reverse reaction Ea

T(K) CVT CVTI SCT CVT CVTI SCT

200 22.1 13.5 11.2 2.6250 21.9 15.4 11.1 4.6300 21.7 17.1 11.0 6.4350 21.6 18.3 10.9 7.6400 21.5 18.9 11.0 8.4450 21.5 19.4 10.9 8.8500 21.4 19.8 10.9 9.3600 21.4 20.3 11.0 9.8800 21.5 20.7 11.1 10.4

BELL ET AL.

an NSF Young Investigator Award to T. N. T. andNSF Grant No. 9116286to J. S.

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874 VOL. 63, NO. 4